PAC-Bayes Unleashed: Generalisation Bounds with Unbounded Losses

We present new PAC-Bayesian generalisation bounds for learning problems with unbounded loss functions. This extends the relevance and applicability of the PAC-Bayes learning framework, where most of the existing literature focuses on supervised learning problems with a bounded loss function (typically assumed to take values in the interval [0;1]). In order to relax this classical assumption, we propose to allow the range of the loss to depend on each predictor. This relaxation is captured by our new notion of HYPothesis-dependent rangE (HYPE). Based on this, we derive a novel PAC-Bayesian generalisation bound for unbounded loss functions, and we instantiate it on a linear regression problem. To make our theory usable by the largest audience possible, we include discussions on actual computation, practicality and limitations of our assumptions.     

A Clustering Search metaheuristic for the Point-Feature Cartographic Label Placement Problem

The Point-Feature Cartographic Label Placement (PFCLP) problem consists of placing text labels to point features on a map avoiding overlaps to improve map visualization. This paper presents a Clustering Search (CS) metaheuristic as a new alternative to solve the PFCLP problem. Computational experiments were performed over sets of instances with up to 13,206 points. These instances are the same used in several recent and important researches about the PFCLP problem. The results enhance the potential of CS by finding optimal solutions (proven in previous works) and improving the best-known solutions for instances whose optimal solutions are unknown so far.     

Separation of Dirac's Hamiltonian by Van Vleck transformation

ABSTRACT

The now classic Foldy–Wouthuysen transformation (FWT) was introduced as successive unitary transformations. This fundamental idea has become the standard in later developments such as the Douglas–Kroll transformation (DKT) – but it is not the only possibility. FWT can be seen as a simple special case of the general Van Vleck transformation (VVT) which besides the successive version has another, known as the canonical because of a series of nice mathematical properties discovered gradually over time. The aim of the present paper is to compare the two approaches – which give identical results in the lower orders, but not in the higher. After having recapitalised both, we apply them to Dirac's Hamiltonian for the electron in a constant electromagnetic field, written with so few assumptions about the operators that the mathematical techniques stand out separated from the terminology of relativistic quantum mechanics. FWT for a free particle is dealt with by a recent geometric approach to VVT. The original FWT is continued through the next non-zero orders. DKT is considered with special weight on equivalent formulations of the generalised and the optimised forms introduced by Wolf, Reiher and Hess.     

Multi-criteria diagnosis of control knowledge for cartographic generalisation

The development of interactive map websites increases the need of efficient automatic cartographic generalisation. The generalisation process, which aims at decreasing the level of details of geographic data in order to produce a map at a given scale, is extremely complex. A classical method for automating the generalisation process consists in using a heuristic tree-search strategy. This type of strategy requires having high quality control knowledge (heuristics) to guide the search for the optimal solution. Unfortunately, this control knowledge is rarely perfect and its evaluation is often difficult. Yet, this evaluation can be very useful to manage knowledge and to determine when to revise it. The objective of our work is to offer an automatic method for evaluating the quality of control knowledge for cartographic generalisation based on a heuristic tree-search strategy. Our diagnosis method consists in analysing the system’s execution logs, and in using a multi-criteria analysis method for evaluating the knowledge global quality. We present an industrial application as a case study using this method for building block generalisation and this experiment shows promising results.     

Linking ArcView™ and XGobi: Insight behind the Front End

Abstract

This article presents aspects of the implementation of a bidirectional link between the Geographic Information System (GIS) ArcView? and the interactive dynamic statistical graphics program XGobi. We describe the main functionality of the link, the underlying remote procedure call (RPC) mechanism, and internal data structures, and discuss topics such as security, concurrency, and linked brushing. We think that these topics are of particular interest to software authors intending to link similar software packages, and software users learning about strengths (and weaknesses) of the implementation of our link.     

Pauli potential functional for spherical inhomogeneous electron liquids generated by a bare Coulomb field

Making use of the spatial generalisation of Kato's theorem, the Pauli potential functional is derived for spherical inhomogeneous electron liquids generated by a bare Coulomb field.